Inverse 3D Microscopy Rendering for Cell Shape Inference With Active Mesh

Traditional methods for biological shape inference, such as deep learning (DL) and active contour models, face important limitations in 3D. DL approaches require large annotated datasets, which are often impractical to obtain, while active contour methods depend on carefully tuned heuristics for intensity attraction and shape regularization. We introduce deltaMic, a novel differentiable 3D renderer for fluorescence microscopy that formulates shape inference as an inverse problem. By leveraging differentiable convolutions, deltaMic simulates the image formation process, integrating a parameterized point spread function (PSF) with a triangle mesh-based representation of biological structures. Unlike DL- or contour-based segmentation, deltaMic directly optimizes both shape and optical parameters to align synthetic and real microscopy images, removing the need for large datasets or sample-specific fine-tuning. To ensure scalability, we implement a GPU-accelerated Fourier transform for triangle meshes along with narrow-band spectral filtering. We show that deltaMic accurately reconstructs cell geometries from both synthetic and diverse experimental 3D microscopy data, while remaining robust to noise and initialization. This establishes a new physics-informed framework for biophysical image analysis and inverse modeling.